If G is a finitely generated abelian group such that G /G t , has rank n,

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If G is a finitely generated abelian group such that G /G_t, has rank n, and H is a subgroup of G such that H/ H_t has rank n-m, then m ≤ n and (G/ H)/(G/ H)_t has rank n - m.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 14, 2023 12:06 PM

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If G is a finitely generated abelian group such that G /G t , has rank n,

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By the Second Isomorphism Theorem we have GH GHt GGt HHt GHt Gt H Note that GHt is a finitely ge...View the full answer

Algebra Graduate Texts In Mathematics 73

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